The objective is to investigate and develop distribution-free methods in areas of application for which standard parametric techniques are inappropriate or too insensitive to violations of underlying assumptions. Much of the work of the Branch lends itself to the nonparametric approach. In sample size studies involving analysis of 2x2 tables, the determination of the minimum detectable risk for a given sample size is often required. Although techniques based on asymptotic results for this have been developed within the Branch, they must ultimately be validated by comparison with an exact technique which is based on the theory of randomization testing. This technique has been developed as part of this project. Another common statistical problem that arises from the work of the Branch is the examination of residuals in linear regression to assess goodness of fit. A test based on the distribution of the variance of the size of runs of positive and negative residuals is a potentially apt instrument for such assessment; a computation based exact distribution of the test statistic has been developed and compared to the existing approximate distribution based on asymptotic results.